Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D53×#2047 |
| Fitting | C53×#2047 ⋊ C2 |
| Sylow | C53 ⋊ C2×#2047 |
1330 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 89 points:
(2,4)(5,8,9,21,10,22,25,36)(6,12,13,29,14,19,23,34)(7,16,17,33,18,20,24,35)(11,26,15,31,27,28,30,32)(37,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39);(5,7,10,18)(6,11,14,27)(8,20,22,16)(9,24,25,17)(12,28,19,26)(13,30,23,15)(21,33,36,35)(29,31,34,32);(1,2)(3,4)(5,6,10,14)(7,15,18,30)(8,19,22,12)(9,23,25,13)(11,24,27,17)(16,32,20,31)(21,29,36,34)(26,33,28,35);(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)(86,87)(88,89)728 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 197362);